Nonlinear Stability in the Generalised Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag

The Nonlinear stability of triangular equilibrium points has been discussed in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. The problem is generalised in the sense that smaller primary is supposed to be an oblate spheroid. The bigger primary is considered as radiating. We have performed first and second order normalization of the Hamiltonian of the problem. We have applied KAM theorem to examine the condition of non-linear stability. We have found three critical mass ratios. Finally we conclude that triangular points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fails.Comment: Including Poynting-Robertson Drag the triangular equilibrium points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fail

Analogue Models for T and CPT Violation in Neutral-Meson Oscillations

Analogue models for CP violation in neutral-meson systems are studied in a general framework. No-go results are obtained for models in classical mechanics that are nondissipative or that involve one-dimensional oscillators. A complete emulation is shown to be possible for a two-dimensional oscillator with rheonomic constraints, and an explicit example with spontaneous T and CPT violation is presented. The results have implications for analogue models with electrical circuits.Comment: 9 page

A dimensionally continued Poisson summation formula

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When combined with one of the proofs of the Jacobi imaginary transformation of theta functions that does not use the Poisson summation formula, our proof of this generalized Poisson summation formula also provides a new proof of the standard Poisson summation formula for dimensions greater than 2 (with appropriate hypotheses on the function being summed). In general, our methods work to establish the (Voronoi) summation formulae associated with functions satisfying (modular) transformations of the Jacobi imaginary type by means of a density argument (as opposed to the usual Mellin transform approach). In particular, we construct a family of generalized theta series from Jacobi theta functions from which these summation formulae can be obtained. This family contains several families of modular forms, but is significantly more general than any of them. Our result also relaxes several of the hypotheses in the standard statements of these summation formulae. The density result we prove for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and improvement

New directions in island biogeography

Aim: Much of our current understanding of ecological and evolutionary processes comes from island research. With the increasing availability of data on distributions and phylogenetic relationships and new analytical approaches to understanding the processes that shape species distributions and interactions, a re-evaluation of this ever-interesting topic is timely. Location: Islands globally. Methods: We start by arguing that the reasons why island research has achieved so much in the past also apply to the future. We then critically assess the current state of island biogeography, focusing on recent changes in emphasis, including research featured in this special issue of Global Ecology and Biogeography. Finally, we suggest promising themes for the future. We cover both ecological and evolutionary topics, although the greater emphasis on island ecology reflects our own backgrounds and interests. Results: Much ecological theory has been directly or indirectly influenced by research on island biotas. Currently, island biogeography is renascent, with research focusing on, among other things, patterns and processes underlying species interaction networks, species coexistence and the assembly of island communities through ecological and evolutionary time. Continuing island research should provide additional insight into biological invasions and other impacts of human activities, functional diversity and ecosystem functioning, extinction and diversification, species pools and more. Deeper understanding of the similarities and differences between island and mainland systems will aid transferability of island theory to continental regions. Main conclusions: As research in biogeography and related fields expands in new directions, islands continue to provide opportunities for developing insights, both as natural laboratories for ecology and evolution and because of the exceptions islands often present to the usual ‘rules’ of ecology. New data collection initiatives are needed on islands world-wide and should be directed towards filling gaps in our knowledge of within-island distributions of species, as well as the functional traits and phylogenetic relationships of island species

The Japanese model in retrospective : industrial strategies, corporate Japan and the 'hollowing out' of Japanese industry

This article provides a retrospective look at the Japanese model of industrial development. This model combined an institutional approach to production based around the Japanese Firm (Aoki's, J-mode) and strategic state intervention in industry by the Japanese Ministry of International Trade and Industry (MITI). For a long period, the alignment of state and corporate interests appeared to match the wider public interest as the Japanese economy prospered. However, since the early 1990s, the global ambitions of the corporate sector have contributed to a significant 'hollowing out' of Japan's industrial base. As the world today looks for a new direction in economic management, we suggest the Japanese model provides policy-makers with a salutary lesson in tying the wider public interest with those of the corporate sector

Cross-ancestry genome-wide association analysis of corneal thickness strengthens link between complex and Mendelian eye diseases

Central corneal thickness (CCT) is a highly heritable trait associated with complex eye diseases such as keratoconus and glaucoma. We perform a genome-wide association meta-analysis of CCT and identify 19 novel regions. In addition to adding support for known connective tissue-related pathways, pathway analyses uncover previously unreported gene sets. Remarkably, >20% of the CCT-loci are near or within Mendelian disorder genes. These included FBN1, ADAMTS2 and TGFB2 which associate with connective tissue disorders (Marfan, Ehlers-Danlos and Loeys-Dietz syndromes), and the LUM-DCN-KERA gene complex involved in myopia, corneal dystrophies and cornea plana. Using index CCT-increasing variants, we find a significant inverse correlation in effect sizes between CCT and keratoconus (r =-0.62, P = 5.30 × 10-5) but not between CCT and primary open-angle glaucoma (r =-0.17, P = 0.2). Our findings provide evidence for shared genetic influences between CCT and keratoconus, and implicate candidate genes acting in collagen and extracellular matrix regulation